Click to download the playlist as a pdf: Liberal Arts Mathematics

PROBLEM SOLVING

Introduction to Percent
Ex 1:  Relating Fractions, Decimals, and Percents
Ex 2:  Relating Fractions, Decimals, and Percents
The Percent Equation
Ex 1: Solve a Percent Problem Using a Percent Equation
Ex 2: Solve a Percent Problem Using a Percent Equation
Ex 3: Solve a Percent Problem Using a Percent Equation
Ex: Determine the Percent of a Number Using a Bar Graph
Ex: Change, Absolute Change, and Relative Change
Percent of Change
Ex 1: Determine a Percent of Change (decrease)
Ex 2: Determine a Percent of Change (increase)
Ex: Tax Percent Application - Find the Amount of FICA tax paid
Ex: Percent Applications - Changing Bases of Relative Change
Ex: Percent of Original Price Paid After Two Percentage Discounts
Ex: Weighted Average - Determine an Ending Percent or Grade of a Weighted Average
Ex: Proportion Application - Estimate Cost Based Upon Area
Ex: Proportion Application - Estimate Cost Based Upon Area
Rates and Unit Rates
American Unit Conversions
Perimeter and Area Formulas
Ex: Find the Number of Meters Traveled in 3 seconds Given Kilometers Per Hour
Unit Conversion Application - Number of Lemons for a Lemon Pie
Ex: Determine the Width of a Canyon Based Upon an Echo Time
Ex: Volume Conversion to Determine the Number of Cubic Yards of Soil Needed

MEASUREMENT / GEOMETRY

Rates and Unit Rates
American Unit Conversions
Metric Unit Conversions
Ex: Find the Number of Meters Traveled in 3 seconds Given Kilometers Per Hour
Unit Conversion Application - Number of Lemons for a Lemon Pie
Ex: Determine the Width of a Canyon Based Upon an Echo Time
Perimeter and Area Formulas
Ex: Volume of a Cylinder
Ex: Volume of a Sphere
Ex 2B: Find the Measure of an Interior Angle of a Triangle

VOTING THEORY

Introduction to Voting Theory and Preference Tables
Ex: Reading a Preference Table (Voting Theory)
Voting Theory:  Fairness Criterion
Voting Theory: Plurality Method and Condorcet Criterion
Ex: Determine the Least Number of Votes Needed Using the Plurality Method
Voting Theory:  Insincere Voting / Strategic Voting
Voting Theory: Instant Runoff Voting
Voting Theory: Monotonicity Criterion Using Instant Runoff Voting
Voting Theory:  Borda count
Voting Theory: Copeland's Method
Voting Theory:  Approval Voting

WEIGHTED VOTING

Introduction to Weighted Voting
Weighted Voting:  Coalitions and Critical Players
Weighted Voting:  The Banzhaf Power Index
Weighted Voting:  The Shapley-Shubik Power Index

FAIR DIVISION

Introduction to Fair Division
Fair Division: The Divider-Chooser Method
The Divider-Chooser Method of Fair Division – Why  It Is Meant Only for 2 Players
Fair Division:  The Lone Divider Method
The Lone Divider Method:  Why It Doesn't Pay To Be Greedy
Fair Division:  The Last Diminisher Method
Fair Division:  The Moving Knife Method
Fair Division:  The Sealed Bid Method

APPORTIONMENT

Introduction to Apportionment
Apportionment:  Hamilton's Method
Apportionment:  The Alabama Paradox
Apportionment:  The New States Paradox
Apportionment:  The Population Paradox
Apportionment:  Jefferson's Method
Apportionment:  Webster's Method
Apportionment:  Huntington-Hill Method
Apportionment:  Lowndes' Method

GRAPH THEORY

Introduction to Graph Theory
Graph Theory:  Dijkstra's Algorithm
Graph Theory:  Euler Paths and Euler Circuits
Graph Theory:  Fleury's Algorthim
Graph Theory:  Eulerization
Graph Theory:  Hamiltonian Circuits and Paths
Graph Theory:  The Brute Force Algorithm
Graph Theory: Number of Routes and Circuits of a Complete Graph
Graph Theory:  Nearest Neighbor Algorithm (NNA)
Graph Theory:  Repeated Nearest Neighbor Algorithm (RNNA)
Graph Theory: Sorted Edges Algorithm (Cheapest Link Algorithm)
Graph Theory: Spanning Trees
Graph Theory:  Kruskal's Algorithm

SCHEDULING

Introduction to Scheduling
Scheduling:  The List Processing Algorithm Part 1
Ex: Scheduling - Create a Priority List Using the Decreasing Time Algorithm
Ex: Scheduling - Create a Priority List Using the Critical Path Algorithm
Scheduling:  The List Processing Algorithm Part 2
Ex: Create a Schedule with Three Processors Using the List Processing Algorithm
Scheduling:  The Decreasing Time Algorithm
Ex: Create a Priority List and Schedule Using the Decreasing Time Algorithm and List Processing Algorithm
Scheduling:  The Critical Path Algorithm Version 1 (Part 1)
Scheduling:  The Critical Path Algorithm Version1 (Part 2)
Scheduling:  The Back Flow Algorithm Part 1
Scheduling:  The Back Flow Algorithm Part 2

GROWTH

Linear Growth:  Recursive and Explicit Equations Part 1
Linear Growth:  Recursive and Explicit Equations Part 2
Ex: Find an Explicit Equation for Linear Growth and Determine and Input for An Output
Ex:  Write an Explicit Equation to Model Linear Growth
Ex: Write a Recursive and Explicit Equation to Model Linear Growth
Exponential Growth:  Recursive and Explicit Equations Part 1
Exponential Growth:  Recursive and Explicit Equations Part 2
Ex: Find an Recursive and Explicit Equation for Exponential Growth Given r
Compare Linear and Exponential Growth Using Recursive and Explicit Equations
Solving Exponential Equations for Time using Common Logs
Logistic Growth: Recursive Equations
Logistic Growth:  Overshoot and Collapse

FINANCE

The Simple Interest Formula
Ex: Determine an Account Balance Using Simple Interest
Compounded Interest
Ex 1: Compounded Interest Formula – Quarterly
Ex: Compounded Interest Formula - Determine Deposit Needed (Present Value)
Solving Exponential Equations for Time using Common Logs
Ex 2: Compounded Interest with Logarithms
Derive the Value of an Annuity Formula
Determining the Value of an Annuity
Determine the Value of an Annuity with a TI84
Payout Annuity Formula - Part 1
Payout Annuity Formula - Part 2
The Installment Loan Formula
The Installment Loan Formula:  Determining Remaining Balance
Annuity Formula and Loan Formula:  Solving for Time
Ex: TI84 TVM Solver - Find the Present Value of a Loan Given Monthly Payment
Ex: TI84 TVM Solver - Present Value with Compounded Interest
TI84 TVM Solver - Find Present Value of an Payout Annuity
Ex: TI84 TVM Solver - Find Payout Annuity Monthly Payment Given Present Value
Ex: TI84 TVM Solver - Find a Monthly Loan Payment
Ex: TI84 TVM Solver - Future Value with Compounded Interest
Ex: TI84 TVM Solver - Find Annuity Monthly Payment Needed for Given Future Value
Ex 1: TI84 TVM Solver - Future Value of an Annuity
Ex 2: TI84 TVM Solver - Future Value of an Annuity

STATISTICS

Introduction to Statistics
Statistics:  Sampling Methods
Statistics Control Groups and the Placebo Effect
Statistics:  Introduction to Experiments and Confounding
Statistics:  Sources of Bias

DESCRIBING DATA

Describing Categorical Data Using a Bar Graph, Pareto Chart, Pie Chart, and Pictogram
Describing Quantitative Data Using a Histogram
Describing Quantitative Data Using Mean, Median, and Mode
Ex: Find the Mean and Median of a Data Set Given in a Frequency Table (odd)
Ex: Find the Mean and Median of a Data Set Given in a Frequency Table (even)
Describing Quantitative Data:  Range and Standard Deviation
Describing Quantitative Data:  Quartiles and the Five Number Summary
Ex: Mode, Mid-range, Range, Standard Deviation Using Range Rule of Thumb
Ex:  Complete a Frequency Table
Ex:  Find the Sample Size and Percent of Sample From a Bar Graph
Ex:  Make a Prediction using the Sample Statistic (Marbles)
Ex:  Determine a Sample Statistics and Make a Prediction using the Statistic
Ex:  Find the Percent of an Amount Using a Percent in Pie Chart
Ex:  Find the a Percent of a Total Using  an Amount in Pie Chart
Describing Quantitative Data using a Box Plot
Ex 1:  Compare Two Box Plot Values
Ex 2:  Compare Two Box Plot Values
Ex:  Determine the Percent Below a Quartile Using a Box Plot
Ex: Determine a Five Number Summary (Odd)
Ex: Determine a Five Number Summary (Even)
Ex: Determine the Five Number Summary from a Box Plot
Ex:  Interpret the Mean and Standard Deviation of Two Data Sets
Ex: Calculate the Sample Standard Deviation
TI84 One Variable Statistics Overview
TI84 One Variable Statistics Overview with Frequency Table
TI84 One Variable Statistics - Five Number Summary
TI84 One Variable Statistics - Mean
TI84 One Variable Statistics - Mean and Median
TI84 One Variable Statistics - Mean and Median Using  a Frequency Table
TI84 One Variable Statistics - Standard Deviation
TI84 One Variable Statistics - Standard Deviation From a Frequency Table

Normal Distribution / Sampling Distribution and Estimations

Introduction to the Normal Distribution
Ex 1: Normal Distribution - Use the Empirical Rule
Ex 2: Normal Distribution - Use the Empirical Rule
Ex 1A (Norm Dist)  Use the 68-95-99.7 Rule to Find the Percent of Data Between Given Data Values
Ex 1B (Norm Dist)  Use the TI84 to Find the Percent of Data Between Given Data Values
Ex 2A (Norm Dist)  Use the 68-95-99.7 Rule to Find the Percent of Data Between Given Data Values
Ex 2B (Norm Dist)  Use the TI84 to Find the Percent of Data Between Given Data Values
Normal Distribution:  Z-Scores
Normal Distribution:  Find Probability Using With Z-scores Using the TI84
Normal Distribution:  Find Probability Using With Z-scores Using Tables
Normal Distribution:  Find Probability of Data Values Using the TI84
Normal Distribution:  Find Probability of Data Values Using Tables
Ex 1:  Find the Probability of a Z-score Being Less Than a Given Value on a Newer TI84
Ex 2:  Find the Probability of a Z-score Being Greater  Than a Given Value on a Newer TI84
Ex 3:  Find the Probability of a Z-score Being Between Two Z-score on a Newer TI84
Ex 1:  Find a Z-score Given the Probability of Z Being Less Than a Given Value
Ex 2:  Find a Z-score Given the Probability of Z Being Greater Than a Given Value
Ex 1: Find a Probability Given a Data Value Involving a Normal Distribution -  P(x<n) TI84
Ex 2: Find a Probability Given a Data Value Involving a Normal Distribution -  P(x>n) TI84
Ex 3: Find a Probability Given a Data Value Involving a Normal Distribution -  P(m<x<n) TI84
Ex 1: Find a Data Value Given a Probability Involving a Normal Distribution - TI84
Ex 2: Find a Data Value Given a Probability Involving a Normal Distribution - TI84

PROBABILITY

Introduction to Probability
Ex:  Basic Example of Finding Probability - Running a Red Light
Ex:  Basic Example of Finding Probability From a Table
Ex: Find Basic Probabilities When Rolling One Fair Die
Ex: Find Basic Probabilities Using a Deck of Cards
Ex: Basic Probability Review Using Marbles
Probability:  The Probability of the Complement of an Event
Probability:  The Probability of Independent Events
Probability:  Determine the Probability of the Union of Events
Probability:  Probability of Mutually Exclusive Events
Probability:  Probability of Events Not Mutually Exclusive
Ex: Determine a Probability with AND using a Table
Ex: Determine the Probability of a Union Using a Table (Not Mutually Exclusive - No Formula)
Ex: Determine the Probability of the Union of Two Events (OR)
Ex: Determine the Probability of a Union Using a Table (Not Mutually Exclusive)
Ex: Find the Probability of a Complement Using a Table
Ex: Find the Probability of Dependent Events Two Ways
Ex 2: Find the Probability of Dependent Events
Probability:  Conditional Probability
Ex: Find Conditional Probability Using a Table
Ex: Determine Conditional Probability from a Table
Probability:  Bayes’ Theorem
The Counting Principle
Simplifying Factorial Expressions
Permutations
Combinations
Counting Problems
Probability:  Determining Probability Using Combinations
Determining Probability
Expected Value
Ex: Expected Value
Ex: Determine Odds from Given Information (Basic)
Ex: Determine Probability Given Odds

HISTORICAL COUNTING SYSTEMS

Inca Counting Boards
The Inca Quipu
Convert Numbers in Different Bases to Base Ten
Ex: Convert Base-12 to Base-10
Convert Numbers in Base Ten to Different Bases:  Remainder Method
Convert Numbers in Base Ten to Different Bases:  Calculator Method
The Mayan Number System: Writing Mayan Number in Base 10
The Mayan Number System: Writing Base 10 Numbers as Mayan Number (base 20)
The Mayan Number System: Addition of Mayan Numbers

CRYPTOGRAPHY

Cryptograph: Substitution Cipher (Caeser Cipher)
Cryptography: Transposition Cipher
Cryptography: Caesar Cipher With Shift
Modular Arithmetic

SETS

Introduction to Set Theory
Introduction to Subsets
Set Operations and Venn Diagrams - Part 1 of 2
Set Operations and Venn Diagrams - Part 2 of 2
Solving Problems Using Venn Diagrams
Ex: Find the Union and Intersection of Two Sets Using a Venn Diagram
Ex: Find the Union and Intersection of Two Sets Without a Venn Diagram
Ex: Find the Intersection of a Set and A Complement Using a Venn Diagram

Ex: Find Intersections and Unions of Three Sets Using a Venn diagram (short)
Ex: Find Intersections and Unions of Three Sets Without Using a Venn diagram (short)
Ex: Find Intersections and Unions of Three Sets Using a Venn diagram (long)
Ex: Find Intersections and Unions of Three Sets Without Using a Venn diagram (long)
Ex: Determine Cardinality of the Intersection of Two Sets Using a Venn Diagram
Ex: Determine Cardinality of the Intersection of Two Sets Without Using Venn Diagram
Ex: Determine Cardinality of Various Sets Given a Venn Diagram of Three Sets
Ex: Determine Cardinality of the Intersection of Three Sets Using a Venn Diagram
Ex: Determine Cardinality of the Intersection of Three Sets Without Using Venn Diagram
Ex:  Find the Number of Element in the Intersection of Two Sets Using a Venn Diagram
Ex: Set Problem Solving - Find the Number of Element in the Intersection of Two Sets Using a Formula
Ex 1: Set Problem Solving - Find the Number of Element in the Union of Two Sets Using a Venn Diagram
Ex 1: Set Problem Solving - Find the Number of Element in the Union of Two Sets Using a Formula
Ex 2:  Find the Number of Element in the Union of Two Sets Using a Venn Diagram
Ex 2: Set Problem Solving - Find the Number of Element in the Union of Two Sets Using a Formula
Ex: Determine How Many Elements in a Set With a Venn Diagram (Movies)
Ex: Determine How Many Elements in a Set Without a Venn Diagram (Movies)
Ex 1:  Problem Solving With Venn Diagrams (Cardinality of Intersection)
Ex 2:  Problem Solving With Venn Diagrams (Cardinality of A Intersect B Complement)
Ex 3:  Problem Solving With Venn Diagrams (Cardinality of Complement of (A Union B)
Ex 4:  Problem Solving With Venn Diagrams (Cardinality of A Intersect B Complement)

Logic

If-Then Statements and Converses
The Converse, Contrapositive, and Inverse of an If-Then Statement
Truth Tables for Compound Statements
Truth Tables for Conditional Statements
Truth Table for the Biconditional Statement
Truth Tables:  Showing Statements are Equiv

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